The invention concern a skiving machine for hides and similar materials, comprising a dished cutter rotary supported by a horizontal shaft, a feeding roller for material close to the cutting edge of the dished cutter and a presser element for the material on the feeding roller, adjustably supported with respect to the roller. The hide, leather or similar material must undergo preliminary skiving around the edges prior to folding, cementing or sewing. The angle and shape of the skiving depend, apart from the thickness of the material, upon other characteristics of the article in leather or similar material, and may vary according to the features of the cutting unit and of the feeding roller on the skiving machine.